Least squares finite element simulation of local transfer for a generalized Newtonian fluid in 2D periodic porous media.

In this paper, the asymptotic homogenization method is applied to the filtration theory of a generalized Newtonian fluid in periodic porous media. The asymptotic expansion of non-Newtonian viscosity is obtained by the asymptotic expansion of the second invariant of the strain tensor. The so-called local problem in periodic cells is presented to describe the microscale transport of a generalized Newtonian fluid in porous media. Based on nonlinear tensor function theory, the filtration law of generalized Newtonian fluid is obtained, which is used to describe the average process of filtration. A new numerical method to solve the local problem is proposed by using the least squares finite element method, and the permeability coefficient and effective viscosity of a generalized Newtonian fluid in porous media are evaluated. The exact solution of Poiseuille's flow in the microtube for a power-law fluid is obtained by theoretical analysis to verify the accuracy of the proposed model. Finally, the local transports of a shear-thinning Modified Cross fluid in two classical 2D porous structures are simulated and the dependencies of the permeability tensor and effective viscosity on the pressure gradient in porous structures are analyzed, which validates the proposed models and numerical methods. • A local problem on periodic cells is presented for the flow of a generalized Newtonian fluid in a single pore. • Developed the least squares finite element method to solve local problems. • The filtration law of a generalized Newtonian fluid is proposed using nonlinear tensor function theory. • Exact solutions for Poiseuille's flow of a power-law fluid in microtubes are obtained. • Local problems are solved and the permeability and effective viscosity in 2D porous structures are obtained. [ABSTRACT FROM AUTHOR]